Nanoparticles are currently the subject of intense study as surveyed, for example, in G. Schmid, ed., Nanoparticles: From Theory to Application (Wiley, 2004), which is incorporated herein by reference. Applications are as diverse as drug delivery, sensing, bio-imaging and sorbent manufacture. Not least among the interesting properties of nanoparticles are their optical characteristics. The optical attributes of nanoparticles are observed in familiar materials such as opal and stained glass. More recently the optical properties of nanostructures have been exploited in applications such as the construction of metamaterials, discussed by Ziolkowski et al., eds., Metamaterials: Physics and Engineering Explorations (Wiley, 2006), and the subwavelength containment of fields using optical antennas, as discussed by Miihlschlegel et al., Resonant optical antennas, Science, 308, 1607-1609 (2005). With the increasing use of nanoparticles in optical applications it is desirable to be able to characterize the optical response of a single nanoparticle. This work focuses on the elastic scattering properties of a nanoparticle, as manifested by a wavelength-dependent susceptibility tensor, which expresses the relationship between polarization of the particle and electric fields: linear in the case of polarizability, and to successive orders of the field, when non-linear contributions are considered.
The susceptibility of a nanoparticle is determined both by the constituent material and by the particle size and shape. For purposes of the present description, unless the particular context requires otherwise, the term “nanoparticle” will refer to a scatterer having point-like characteristics, in that its overall dimensions are smaller than the diffraction limit of any radiation used in its characterization. For a known material and geometry, the polarizability may be determined analytically or by computational methods, and so may non-linear terms, in principle. However, small deviations from the specified shape may introduce significant optical changes. See Canfield et al., Chirality arising from small defects in gold nanoparticle arrays, Opt. Express 14, 950-955 (2006) for a discussion of related measurements from nanoparticle arrays. It is, therefore, highly desirable that methods be provided for actually measuring terms of the susceptibility using far-field optical measurements. Such methods are provided by the current invention, as discussed below.
To date, limited effort has been placed on determining the elements of the second-order nonlinear susceptibility tensor for individual nanoparticles. Yet, it has been demonstrated with biological samples that the determination of the tensor elements provides additional information about the nanoparticles and may be useful in fields like bioimaging, sensing, drug delivery, and imaging, more generally.
The measurement scheme of the present invention is based on improvements to a coherent confocal microscope. Coherent microscopes use interference with a reference beam to holographically record data and hence acquire information regarding the phase of the measured field. While coherent microscopy predates the invention of the laser, modern bright and broadband sources have made spectrally-sensitive coherent microscopy a practical methodology. This is evidenced by the popularity of techniques such as optical coherence tomography (OCT).
In addition to collecting phase-sensitive data, a coherent microscope has the advantage of high sensitivity when compared to a traditional intensity-based system. As a result, coherent microscopy is suitable for true nanoimaging, as demonstrated by results such as the interferometric detection of single viruses and gold particles as small as 5 nm, as reported by Ignatovich et al., Real-time and background-free detection of nanoscale particles, Phys. Rev. Lett., 96, article no. 013,901 (2006).
In coherent microscopy the optical source is usually split into a reference field and a field that is used to illuminate the sample. The light returned from the sample is combined with the reference field and the interferometric features in the data are used for image formation. To exhibit interference the returned light must be coherent with the reference field and at the same frequency. This means that potentially useful signals from a nanoparticle, such as Raman-scattered, higher-harmonic and/or fluorescent light, are not detected. In more generalized coherent microscopy, the reference field may be light that is derived coherently from the optical source used to illuminate the sample.
Second-harmonic generation (SHG) is a coherent second-order non-linear optical process which produces an optical field at twice the frequency of the input (pump) field; this process occurs only in noncentrosymmetric material systems. The second-order nonlinear susceptibility that describes the generation of the SHG signal depends on the electronic configurations, molecular structures and alignments, and local morphologies of the system. As a result, SHG has been successfully used to investigate the local molecular alignment and/or the structure in a wide variety of materials including biological tissues, organic and inorganic crystals, molecular materials, and surfaces and interfaces. SHG has also been used to characterize individual nanoparticles, as discussed, for example, in Sandeau et al., Defocused imaging of second harmonic generation from a single nanocrystal, Opt. Express, 15, 16051 (2007), which is incorporated herein by reference. In one study, the orientation and the crystalline nature of the individual organic nanocrystals were inferred from the SHG signal together with the two-photon excited fluorescence, reported by Brasselet et al., In-situ diagnostics of the crystalline nature of single organic nanocrystals by nonlinear microscopy, Phys. Rev. Lett., 22, 207401 (2004), which is also incorporated herein by reference. In another study, three-dimensional orientation of the individual nanocrystals was determined by imaging the emitted SHG signal using a defocused imaging system
Traditional microscopy and spectroscopy usually involve the formation of a scalar image on spatial and/or spectral axes. While this image is immediately useful in many applications, it is possible to design sensing systems that form non-scalar images and/or exploit less obvious relationships between the collected data and the imaged objects. A comprehensive discussion is provided by Barrett et al., Foundations of Image Science (Wiley-Interscience, 2003), which is incorporated herein by reference. For example, many modern microscopy and imaging systems collect images as a function of polarization state and/or scattering angle. Additionally, in some applications the object can be represented by a small number of parameters which are estimated from the data with very high precision. In single molecule microscopy, the a priori knowledge that the object can be parameterized by the molecule location allows the molecule to be localized with a precision orders of magnitude better than the diffraction limit.